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It depends on the fraction. For the following, assume the denominator is not zero, for if it is, then the fraction is undefined.

  • If the numerator and denominator are both rational, then the fraction is rational.
  • If one of them is rational and the other is irrational then (provided the numerator is not 0), the fraction is irrational.
  • If both are irrational you need to simplify first and then apply one of the above two criteria.

For example, sqrt(2)/sqrt(8) = sqrt(2/8) = sqrt(1/4) = ±1/2. So, irrational/irrational

can be rational.

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Q: Is a fraction a rational or irrational number?
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